Page 532 - Algebra 1

L E S S O N Factoring Trinomials by Using the GCF 79
Warm Up
1. Vocabulary A is the sum or difference of monomials. (53)
Factor.
2.x2 +3x-10
(72)
4.-11x-21+2x2 (75)
3.-13p+p2 +36 (72)
5.5x2 -13x-6 (75)
New Concepts The terms of a polynomial that is factored completely will have no common factors other than 1. To factor completely, begin by factoring out the greatest
common factor, or GCF.
Factoring Trinomials with Positive Leading Coefficients
Factor completely.
a. x4 +5x3 +6x2
SOLUTION
Find the GCF of the terms. In this case, x2 is the GCF.
x4 +5x3 +6x3
x2(x2 + 5x + 6) Factor out the GCF.
Find two numbers that have a product of 6 and a sum of 5. 2 · 3 = 6 and 2 + 3 = 5
x2(x2 +5x+6)=x2(x+2)(x+3)
So,x4 +5x3 +6x2 =x2(x+2)(x+3).
b. 4x3 -4x2 -80x
SOLUTION
The GCF of the terms is 4x.
4x3 - 4x2 - 80x
4x(x2 - x - 20) Factor out the GCF.
Find two numbers that have a product of -20 and a sum of -1. 4 · -5 = -20 and 4 + (-5) = -1
4x(x2 -x-20)=4x(x+4)(x-5)
So,4x3 -4x2 -80x=4x(x+4)(x-5).
When the leading coefficient is negative, factor out a -1.
Example
1
Caution
Include the GCF in the final factored form. The factored form equals the original trinomial if its factors are multiplied.
Math Language
The leading coefficient is the coefficient of the term with the greatest degree.
Lesson 79 517